arXiv subjects

Ioannis Anagnostides

Publications and source records attributed to Ioannis Anagnostides.

At least 19 recordsLinked to original sources

arXiv2026

Algorithmic Collusion and the Complexity of Information-Value-Free Equilibria

A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing to a fixed action. Motivated by the problem of regulating algorithmic collusion, this refinement was introduced by Hartline, Wang, and Zhang [EC'26], who showed that it can be computed in polynomial time in explicitly represented normal-form game. In this paper, we examine the complexity of IVF(C)CEs in succinct games, which model more realistic strategic interactions that feature either many players or exponentially many pure strategies. We first show that computing an information-value-free CE is PPAD-complete in many-player polymatrix games or two-player Bayesian games, even when the approximation is a constant. We also prove an unconditional exponential query lower bound. Our results establish that IVFCEs are intractable, even in the centralized model, and rule out the existence of any efficient learning dynamics. This significantly strengthens the impossibility result of Hartline, Wang, and Zhang, which concerns a particular class of learning algorithms, and furnishes strong computational critiques of recent regulation on algorithmic collusion. To sidestep these hardness results, we examine the complexity of information-value-free CCE. Certain no-regret algorithms---such as regret matching or FTRL---provide a fully polynomial-time approximation scheme (FPTAS) for this problem. The complexity when the approximation is exponentially small turns out to be nuanced. On the one hand, leveraging no-regret dynamics, we establish membership in $\text{CLS} = \text{PPAD} \cap \text{PLS}$. On the other hand, we show that it is at least as hard as the P-matrix linear complementarity problem, and hence as hard as simple stochastic games. This shows that even IVFCCEs are unlikely to admit a polynomial-time algorithm barring a major breakthrough.

cs.GT↗

arXiv2026

From Compensation Design to Budget-Feasible Mechanisms: A Constant Approximation for Subadditive Valuations

Budget-feasible mechanism design is a classic framework introduced by Singer, but there is still a wide gap between existing upper and lower bounds. In this paper, we significantly advance the state of the art. First, without computational constraints, we show that there exists a universally truthful budget-feasible mechanism with the following approximation ratios: - $3$ for monotone submodular valuations and $e+1$ for nonmonotone submodular valuations, improving over $3.798$ and $9.742$, respectively. - $e+1$ for XOS valuations, improving over $28$. In large markets, our approximation can be improved deterministically to $e$. - $2e+1$ for subadditive valuations, improving over $33$. In large markets, our approximation can be improved deterministically to $2e$. Moreover, for subadditive valuations, we obtain a constant-approximation mechanism that runs in polynomial time using demand queries. This improves over the previous best approximation of $O(\log \log n)$, resolving a long-standing open problem going back to Dobzinski, Papadimitriou, and Singer, who conjectured that a constant approximation requires exponentially many demand queries. We obtain these results through a simple and unifying framework based on non-truthful indirect mechanisms, recently coined compensation design. In particular, through a potential argument, we establish constant price-of-stability bounds for compensation design based on marginal-contribution payment rules, which we then translate into truthful direct mechanisms. For subadditive valuations, the core of the argument is a new smoothing lemma showing that every subadditive function can be approximated within a factor of $2$ by a self-bounding function. This is also of independent interest, readily addressing an open question in multiwinner elections by showing the existence of a $2e$-approximate core even under subadditive valuations.

cs.GT↗

arXiv2026

Preference Elicitation for Policy Optimization and Application to Aligning Heart Transplantation with Human Values

Preference elicitation is essential for aligning AI systems with human values. Prior approaches (e.g., for organ allocation) often ask stakeholders to compare the decisions of an algorithm (e.g., patient A vs. patient B). Such a decision-level approach conflates the means with the ends. Instead, we elicit preferences directly over allocation outcomes to learn a utility function for policy optimization. We construct a novel preference elicitation algorithm for linear utilities that outperforms prior techniques in practice. Our algorithm has two phases. The first phase learns cutting planes through pairwise comparisons to rapidly shrink the space of possible attribute weights and warm-starts the second phase by eliminating dominated regions. The second phase then provably converges to the user's utility function. We apply our technique to heart transplant allocation where a policy must balance competing objectives such as post-transplant outcomes, waitlist mortality, geographic ease, and equity. Using our algorithm, we conduct a user study to learn and aggregate a community-aligned utility function, and use it to optimize heart transplant policies that are significantly better aligned with human values. Compared to the hindsight optimum, the status quo policy achieves a competitive ratio of just 0.54, while our method is near-optimal with a competitive ratio of 0.95.

cs.AI↗

arXiv2026

Compensation Design

We introduce compensation design, the problem of designing payment rules that incentivize high-quality contributions in decentralized environments. Here, a budget-constrained principal with a monotone submodular value function aims to design a payment rule, while agents decide whether to opt in or out depending on their private cost. We show that a simple cost-oblivious and anonymous marginal-contribution payment rule guarantees that pure Nash equilibria always exist and attain a price of anarchy (PoA) of at most $2+o_λ(1)$ in the large-market regime ($λ\to 0$) where each individual cost is at most a $λ$ fraction of the budget. We further show that the factor $2$ is unavoidable among deterministic cost-oblivious rules. Surprisingly, we identify a counterexample showing that a payment rule based on the Shapley value may admit no pure Nash equilibria. We then extend our scope to coarse correlated equilibria. This is further motivated by our intractability result: although a pure Nash equilibrium always exists, computing one is PLS-complete. We establish that coarse correlated equilibria also attain a PoA bound of at most $2+o_λ(1)$, and this guarantee in fact extends even under the payment rule induced by the Shapley value. Moreover, we move beyond monotone submodular value functions and binary actions. First, for (monotone) XOS valuations, we show that no oracle-efficient payment rule can attain a PoA bound of $O(n^{1/2 - ε})$. Second, for submodular but non-monotone valuations, we show that a broad class of natural payment rules fails to guarantee a bounded PoA. Finally, we extend compensation design to the setting where each agent has a combinatorial action set. We provide randomized payment rules with logarithmic PoA guarantees for subadditive values, and matching lower bounds that apply even in the single-agent additive-value setting.

cs.GT↗

arXiv2026

The Computational Complexity of Team Zero-Sum Games

A celebrated consequence of the minimax theorem is that two-player zero-sum games admit a tractable equilibrium characterization. In many central applications, however, each side comprises multiple independent agents who share a common objective but cannot perfectly coordinate their actions. Such settings can be modeled as \emph{team zero-sum games}, a natural generalization of both two-player zero-sum games and potential games -- the two most well-studied classes of games in algorithmic game theory. In this paper, we settle the complexity of team zero-sum games by establishing that computing Nash equilibria is \PPAD-complete. As a result, despite the global adversarial structure, team zero-sum games are as hard as general-sum games. Our hardness result holds even when i) the precision is inverse polynomial, thereby ruling out a fully polynomial-time approximation scheme (unless $¶= \PPAD$); ii) each team consists of only two players; and iii) the underlying class of games is polymatrix. As a byproduct, we resolve the complexity of group-wise zero-sum polymatrix games, a class introduced and examined in the seminal work of Cai and Daskalakis (SODA '11), and more recently highlighted by Hollender, Maystre, and Nagarajan (ICLR '25). Moreover, we show that computing a first-order stationary point in min-max optimization is \PPAD-complete even for quadratic (multilinear) objectives. From a technical standpoint, we develop a series of team zero-sum game gadgets that allow us to simulate the breakthrough reduction of Bernasconi and Castiglioni (STOC '26). Moreover, to obtain hardness results for quadratic objectives, we make use of a general technique based on linear local approximation, which is of independent interest.

cs.GT↗

arXiv2026

Aligning Data-Driven Predictors with Allocation: A Decision-Focused Approach to Survival Analysis

Machine learning predictors have become essential tools for guiding automated decision making. However, a major misalignment persists: predictive models are typically optimized in terms of standard statistical metrics in isolation from the algorithmic tasks they inform. We highlight this incongruity in the high-stakes domain of organ allocation by demonstrating that any algorithm relying on (even highly accurate) survival predictors optimized for standard metrics -- such as the Concordance index (C-index) -- can yield arbitrarily poor outcomes when used for allocation, failing to guarantee utility better than a uniform random selection. To bridge the gap between survival analysis and policy optimization, we introduce a decision-focused learning approach based on optimizing normalized discounted cumulative gain (NDCG), a mainstay metric in information retrieval. We establish the utility of NDCG in survival analysis by proving that it translates to guarantees on the performance of allocation. Empirically, we propose a bootstrapping approach to optimize the NDCG of existing survival models. Unlike prior work, we also address the challenge of right censorship when evaluating ranking. On historical heart transplant data from the US, our method dramatically boosts the NDCG of baseline models by 50-100%, which translates to tens of thousands of additional life years gained annually when deployed for transplant allocation. We anticipate that our framework will find broader applications in decision making with predictions.

cs.LG↗

arXiv2026

Position: Machine Learning for Heart Transplant Allocation Policy Optimization Should Account for Incentives

The allocation of scarce donor organs constitutes one of the most consequential algorithmic challenges in healthcare. While the field is rapidly transitioning from rigid, rule-based systems to machine learning and data-driven optimization, we argue that current approaches often overlook a fundamental barrier: incentives. In this position paper, we highlight that organ allocation is not merely an optimization problem, but rather a complex game involving organ procurement organizations, transplant centers, clinicians, patients, and regulators. Focusing on US adult heart transplant allocation, we identify critical incentive misalignments across the decision-making pipeline, and present data showing that they are having adverse consequences today. Our main position is that the next generation of allocation policies should be incentive aware. We outline a research agenda for the machine learning community, calling for the integration of mechanism design, strategic classification, causal inference, and social choice to ensure robustness, efficiency, fairness, and trust in the face of strategic behavior from the various constituent groups.

cs.LG↗

arXiv2026

Swap Regret Minimization Through Response-Based Approachability

We consider the problem of minimizing different notions of swap regret in online optimization. These forms of regret are tightly connected to correlated equilibrium concepts in games, and have been more recently shown to guarantee non-manipulability against strategic adversaries. The only computationally efficient algorithm for minimizing linear swap regret over a general convex set in $\mathbb{R}^d$ was developed recently by Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25). However, it incurs a highly suboptimal regret bound of $Ω(d^4 \sqrt{T})$ and also relies on computationally intensive calls to the ellipsoid algorithm at each iteration. In this paper, we develop a significantly simpler, computationally efficient algorithm that guarantees $O(d \sqrt{T})$ linear swap regret for a general convex set that has been preconditioned via the John ellipsoid. Our algorithm leverages the powerful response-based approachability framework of Bernstein and Shimkin (JMLR~'15) -- previously overlooked in the line of work on swap regret minimization -- and simultaneously minimizes profile swap regret, which was recently shown to guarantee non-manipulability. Moreover, we establish a matching information-theoretic lower bound: any learner must incur in expectation $Ω(d \sqrt{T})$ linear swap regret for large enough $T$, even when the set is centrally symmetric. This also shows that the classic algorithm of Gordon, Greenwald, and Marks (ICML '08) is existentially optimal for minimizing linear swap regret, although it is computationally inefficient. Finally, we extend our approach to minimize regret with respect to the set of swap deviations with polynomial dimension, unifying and strengthening recent results in equilibrium computation and online learning.

cs.LG↗

arXiv2026

On the Complexity of Correlated Equilibria Beyond Normal-Form Games

Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly concave games -- has remained a major open problem, first highlighted by Papadimitriou and Roughgarden (JACM '08). In this paper, we resolve several long-standing questions concerning the complexity of correlated equilibria and swap regret minimization. First, we show that computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping (Contr), providing the first strong evidence of intractability. Moreover, we establish an unconditional, information-theoretic lower bound ruling out the existence of a strongly sublinear swap regret minimizer: any online learning algorithm requires exponentially many iterations in the dimension $d$ to guarantee at most $1/\text{poly}(d)$ (average) swap regret. To circumvent these hardness results, we examine the complexity of $Φ$-equilibria -- tractable relaxations of correlated equilibria. We obtain a fully polynomial-time approximation scheme (FPTAS) for computing poly-dimensional $Φ$-equilibria in general concave games. We complement this by showing that Contr-hardness persists even under poly-dimensional swap deviations in the regime where the precision $ε$ is exponentially small. Finally, we show that Contr-hardness can be bypassed in the canonical setting of concave \emph{quadratic games}, for which we provide a $\text{poly}(d, \log(1/ε))$-time algorithm for computing poly-dimensional $Φ$-equilibria. As a byproduct, we obtain an algorithm for computing fixed points of a mapping that is contracting with respect to an unknown Mahalanobis norm, which could be of independent interest.

cs.GT↗

arXiv2026

A Polynomial-Time Algorithm for Variational Inequalities under the Minty Condition

Solving (Stampacchia) variational inequalities (SVIs) is a foundational problem at the heart of optimization. However, this expressivity comes at the cost of computational hardness. As a result, most research has focused on carving out specific subclasses that elude those intractability barriers. A classical property that goes back to the 1960s is the Minty condition, which postulates that the Minty VI (MVI) problem admits a solution. In this paper, we establish the first polynomial-time algorithm -- with complexity growing polynomially in the dimension $d$ and $\log(1/ε)$ -- for solving $ε$-SVIs for Lipschitz continuous mappings under the Minty condition. Prior approaches either incurred an exponentially worse dependence on $1/ε$ (and other natural parameters of the problem) or made more restrictive assumptions, such as monotonicity. To do so, we introduce a new variant of the ellipsoid algorithm whereby separating hyperplanes are obtained after taking a descent step from the center of the ellipsoid. It succeeds even though the set of SVIs can be nonconvex and not fully dimensional. Moreover, when our algorithm is applied to an instance with no MVI solution and fails to identify an SVI solution, it produces a succinct certificate of MVI infeasibility. We also show that deciding whether the Minty condition holds is $\mathsf{coNP}$-complete, thereby establishing that the disjunction of those two problems is polynomial-time solvable even though each problem is individually intractable. We provide several extensions and new applications of our main results. Most notably, we obtain the first polynomial-time algorithms for computing Nash equilibria in multi-player harmonic games. Finally, in two-player general-sum concave games, we give the first polynomial-time algorithm that outputs either a Nash equilibrium or a strict coarse correlated equilibrium.

math.OC↗

arXiv2026

Steering No-Regret Learners to a Desired Equilibrium

A mediator observes no-regret learners playing an extensive-form game repeatedly across $T$ rounds. The mediator attempts to steer players toward some desirable predetermined equilibrium by giving (nonnegative) payments to players. We call this the steering problem. The steering problem captures problems several problems of interest, among them equilibrium selection and information design (persuasion). If the mediator's budget is unbounded, steering is trivial because the mediator can simply pay the players to play desirable actions. We study two bounds on the mediator's payments: a total budget and a per-round budget. If the mediator's total budget does not grow with $T$, we show that steering is impossible. However, we show that it is enough for the total budget to grow sublinearly with $T$, that is, for the average payment to vanish. When players' full strategies are observed at each round, we show that constant per-round budgets permit steering. In the more challenging setting where only trajectories through the game tree are observable, we show that steering is impossible with constant per-round budgets in general extensive-form games, but possible in normal-form games or if the per-round budget may itself depend on $T$. We also show how our results can be generalized to the case when the equilibrium is being computed online while steering is happening. We supplement our theoretical positive results with experiments highlighting the efficacy of steering in large games.

cs.GT↗

arXiv2026

Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games

A considerable chasm has been looming for decades between theory and practice in zero-sum game solving through first-order methods. Although a convergence rate of $T^{-1}$ has long been established, the most effective paradigm in practice is counterfactual regret minimization (CFR), which is based on regret matching and its modern variants. In particular, the state of the art across most benchmarks is predictive regret matching$^+$ (PRM$^+$). Yet, such algorithms can exhibit slower $T^{-1/2}$ convergence even in self-play. In this paper, we close the gap between theory and practice. We propose a new scale-invariant and parameter-free variant of PRM$^+$, which we call IREG-PRM$^+$. We show that it achieves $T^{-1/2}$ best-iterate and $T^{-1}$ (i.e., optimal) average-iterate convergence guarantees, while also being on par or even better relative to PRM$^+$ on benchmark games. From a technical standpoint, we draw an analogy between (IREG-)PRM$^+$ and optimistic gradient descent with adaptive learning rate. Reflecting this theoretical bridge, we find that the adaptive version of optimistic gradient descent we consider performs on par with IREG-PRM$^+$. This demystifies the effectiveness of the regret matching family vis-a-vis more standard optimization techniques. Moreover, we extend our analysis beyond zero-sum games to a family of variational inequality problems that includes harmonic games, as well as extensive-form games with fully-mixed equilibria, via a new and intriguing connection between CFR and harmonic games. Unlike prior work in harmonic games, our algorithms do not require knowing the underlying weights by virtue of scale invariance. Under the weighted Minty condition, we show that any algorithm satisfying a scale-invariant RVU property (such as IREG-PRM$^+$) has constant regret (in self-play) and $T^{-1/2}$ iterate convergence.

cs.GT↗

arXiv2026

Decision Making under Imperfect Recall: Algorithms and Benchmarks

In game theory, imperfect-recall decision problems model situations in which an agent forgets information it held before. They encompass games such as the ``absentminded driver'' and team games with limited communication. In this paper, we introduce the first benchmark suite for imperfect-recall decision problems. Our benchmarks capture a variety of problem types, including ones concerning privacy in AI systems that elicit sensitive information, and AI safety via testing of agents in simulation. Across 61 problem instances generated using this suite, we evaluate the performance of different algorithms for finding first-order optimal strategies in such problems. In particular, we introduce the family of regret matching (RM) algorithms for nonlinear constrained optimization. This class of parameter-free algorithms has enjoyed tremendous success in solving large two-player zero-sum games, but, surprisingly, they were hitherto relatively unexplored beyond that setting. Our key finding is that RM algorithms consistently outperform commonly employed first-order optimizers such as projected gradient descent, often by orders of magnitude. This establishes, for the first time, the RM family as a formidable approach to large-scale constrained optimization problems.

cs.GT↗

arXiv2026

The Complexity of Equilibrium Refinements in Potential Games

The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show that computing a pure(-strategy) perfect or proper equilibrium is $\mathsf{PLS}$-complete in concise potential games in normal form. For pure perfect equilibria, we extend this result to general polytope games, which includes extensive-form games. We next turn to more structured classes of games, namely symmetric network congestion and symmetric matroid congestion games. For both classes, we show that a pure perfect equilibrium can be computed in polynomial time, strengthening the existing results for pure Nash equilibria. More broadly, we make a connection between strongly polynomial-time algorithms and efficient perturbed optimization using fractional interpolation. On the other hand, we establish that, for a certain class of potential games, there is an exponential separation in the length of the best-response path between perfect and Nash equilibria. Finally, for mixed strategies, we prove that computing a point geometrically near a perfect equilibrium requires a doubly exponentially small perturbation even in $3$-player potential games in normal form. As a byproduct, this significantly strengthens and simplifies a seminal result of Etessami and Yannakakis (FOCS '07). On the flip side, in the special case of polymatrix potential games, we show that equilibrium refinements are amenable to perturbed gradient descent dynamics, thereby belonging to the complexity class $\mathsf{CLS}$. This provides a principled and practical way of refining the landscape of gradient descent in constrained optimization.

cs.GT↗

arXiv2026

The Complexity of Proper Equilibrium in Extensive-Form and Polytope Games

The proper equilibrium, introduced by Myerson (1978), is a classic refinement of the Nash equilibrium that has been referred to as the "mother of all refinements." For normal-form games, computing a proper equilibrium is known to be PPAD-complete for two-player games and FIXP$_a$-complete for games with at least three players. However, the complexity beyond normal-form games -- in particular, for extensive-form games (EFGs) -- was a long-standing open problem first highlighted by Miltersen and Sørensen (SODA '08). In this paper, we resolve this problem by establishing PPAD- and FIXP$_a$-membership (and hence completeness) of normal-form proper equilibria in two-player and multi-player EFGs respectively. Our main ingredient is a technique for computing a perturbed (proper) best response that can be computed efficiently in EFGs. This is despite the fact that, as we show, computing a best response using the classic perturbation of Kohlberg and Mertens based on the permutahedron is #P-hard even in Bayesian games. In stark contrast, we show that computing a proper equilibrium in polytope games is NP-hard. This marks the first natural class in which the complexity of computing equilibrium refinements does not collapse to that of Nash equilibria, and the first problem in which equilibrium computation in polytope games is strictly harder -- unless there is a collapse in the complexity hierarchy -- relative to extensive-form games.

cs.GT↗

arXiv2026

Learning Potentials for Dynamic Matching and Application to Heart Transplantation

Each year, thousands of patients in need of heart transplants face life-threatening wait times due to organ scarcity. While allocation policies aim to maximize population-level outcomes, current approaches often fail to account for the dynamic arrival of organs and the composition of waitlisted candidates, thereby hampering efficiency. The United States is transitioning from rigid, rule-based allocation to more flexible data-driven models. In this paper, we propose a novel framework for non-myopic policy optimization in general online matching relying on potentials, a concept originally introduced for kidney exchange. We develop scalable and accurate ways of learning potentials that are higher-dimensional and more expressive than prior approaches. Our approach is a form of self-supervised imitation learning: the potentials are trained to mimic an omniscient algorithm that has perfect foresight. We focus on the application of heart transplant allocation and demonstrate, using real historical data, that our policies significantly outperform prior approaches -- including the current US status quo policy and the proposed continuous distribution framework -- in optimizing for population-level outcomes. Our analysis and methods come at a pivotal moment in US policy, as the current heart transplant allocation system is under review. We propose a scalable and theoretically grounded path toward more effective organ allocation.

cs.LG↗

arXiv2026

Tight Inapproximability for Welfare-Maximizing Autobidding Equilibria

We examine the complexity of computing welfare- and revenue-maximizing equilibria in autobidding second-price auctions subject to return-on-spend (RoS) constraints. We show that computing an autobidding equilibrium that approximates the welfare-optimal one within a factor of $2 - ε$ is NP-hard for any constant $ε> 0$. Moreover, deciding whether there exists an autobidding equilibrium that attains a $1/2 + ε$ fraction of the optimal welfare -- unfettered by equilibrium constraints -- is NP-hard for any constant $ε> 0$. This hardness result is tight in view of the fact that the price of anarchy (PoA) is at most $2$, and shows that deciding whether a non-trivial autobidding equilibrium exists -- one that is even marginally better than the worst-case guarantee -- is intractable. For revenue, we establish a stronger logarithmic inapproximability, while under the projection games conjecture, our reduction rules out even a polynomial approximation factor. These results significantly strengthen the APX-hardness of Li and Tang (AAAI '24). Furthermore, we refine our reduction in the presence of ML advice concerning the buyers' valuations, revealing again a close connection between the inapproximability threshold and PoA bounds. Finally, we examine relaxed notions of equilibrium attained by simple learning algorithms, establishing constant inapproximability for both revenue and welfare.

cs.GT↗

arXiv2026

Chaos in Autobidding Auctions

As autobidding systems increasingly dominate online advertising auctions, characterizing their long-term dynamical behavior is brought to the fore. In this paper, we examine the dynamics of autobidders who optimize value subject to a return-on-spend (RoS) constraint under uniform bid scaling. Our main set of results show that simple autobidding dynamics can exhibit formally chaotic behavior. This significantly strengthens the recent results of Leme, Piliouras, Schneider, Spendlove, and Zuo (EC '24) that went as far as quasiperiodicity. Our proof proceeds by establishing that autobidding dynamics can simulate -- up to an arbitrarily small error -- a broad class of continuous-time nonlinear dynamical systems. This class contains as a special case Chua's circuit, a classic chaotic system renowned for its iconic double scroll attractor. Our reduction develops several modular gadgets, which we anticipate will find other applications going forward. Moreover, in discrete time, we show that different incarnations of mirror descent can exhibit Li-Yorke chaos, topological transitivity, and sensitivity to initial conditions, connecting along the way those dynamics to classic dynamical systems such as the logistic map and the Ricker population model. Taken together, our results reveal that the long-term behavior of ostensibly simple second-price autobidding auctions can be inherently unpredictable and complex.

cs.GT↗